The area of a rectangular field is 150 sq. units. If its perimeter is 50 units, its dimensions are ______

Given:

The area of a rectangular field is 150 sq. units.

Its perimeter is 50 units.

Concept used:

1. (A + B)2 = (A - B)2 + 4AB

2. Area of a rectangle = Length × Breadth

3. Perimeter of rectangle = 2(Length + Breadth)

Calculation:

Let the breadth and length of the rectangle be B and L respectively.

According to the concept,

LB = 150      ....(1)

2(L + B) = 50

⇒ (L + B) = 25      ....(2)

⇒ (L + B)² = 25​²

⇒ (L - B)² + 4LB = 625

⇒ (L - B)² = 625 - 4 × 150

⇒ (L - B)² = 25

⇒ (L - B) = 5      ....(3)

So, (2) + (3) we get,

2L = 30

⇒ L = 30/2

⇒ L = 15

Putting L = 15 in (1),

15 × B = 150

⇒ B = 150/15

⇒ B = 10

∴ The dimension of the rectangle is 10, 15.